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Thanks to Edward Ruden who showed the error in my calculation commenting in sci.physics.research. Basically it is the same error mentioned by Carl Brannen in this comment.

The correct formula should be

G = k theta s^2 / 2Mml

We need to suppose that the torque acts on both extremity of the arm so that the torque is 2GMml/s^2.

There is also a problem with the rest point of the arm. I assumed that 20 divisions, as mentioned by Cavendish, is where the neutral position of the arm is. Edward Ruden calculated it from the two extreme points (18.01 18.1 and 24.02 divisions) but I used 21.5 divisions because the first three measurements of the experiment were 21.6, 21.5 and 21.5 divisions.

The result now is much closer to recommended value of G:

G = 5.64243*10^-8

I am not sure if this many digits are justified.

Thanks to everyone who commented and helped.

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